Lesson 30 – Demodulation

Lesson 30 – Demodulation#

Learning Outcomes#

  1. Compute transmitter power efficiency for an AM system with a given modulation index.

  2. Understand block diagram AM demodulators and their limitations.

  3. Analyze envelope detectors in the time domain and synchronous detectors in the frequency domain.

  4. Given an AM modulated signal, design an AM demodulator to recover the original message.

  5. Understand the engineering trade-offs between over- and under-modulated AM communication scenarios.

Demodulation#

The last several lessons have focused on modulation. This lesson focuses on demodulating signals to recover the original information and understanding the associated trade-offs.

Modulation Efficiency#

Previously, we introduced adding a bias signal before modulation. As bias increases, time-domain envelopes separate and a carrier spike appears in the frequency domain.

Two AM types:

  • DSB-SC: Information in sidebands only

  • DSB-LC: Information in sidebands + carrier

Over-modulated

100%-modulated

Under-modulated

\(\alpha \rightarrow \infty\)

\(\alpha = 1\)

\(\alpha = 0.667\)

Efficiency is defined as:

\[ \eta = \frac{\text{useful power}}{\text{total power}} = \frac{P_{USB} + P_{LSB}}{P_{total}} \]

Power:

\[ P = \frac{V_{rms}^2}{R}, \quad V_{rms} = \frac{V_m}{\sqrt{2}}, \quad P = \frac{V_m^2}{2R} \]

With normalized resistance \(R = 1\ \Omega\):

\[ \eta = \frac{\alpha^2}{\alpha^2 + 2} \]

  • DSB-SC: \(\eta = 100\%\)

  • \(\alpha = 1 \Rightarrow \eta = 0.33\)

Envelope Detector#

Under-modulated signals allow envelope detection.

Steps:

  1. Diode (rectification): Removes negative portion

  2. LPF: Removes carrier

  3. HPF: Removes bias

Example Problem 1#

Understand#

Under-modulated → envelope detector works.

Identify#

  • Known: \(T_M = 250\ \mu s\)

  • Unknown: carrier

Plan#

Define LPF and HPF cutoff frequencies.

Solve#

\[ f_M = \frac{1}{T_M} = \frac{1}{250\ \mu s} = 4\ kHz \]

  • LPF cutoff \(> 4\ kHz\)

  • HPF cutoff \(> 0\ Hz\) (use 10 Hz)

Key Takeaways#

  • Diode: removes negative voltages

  • LPF: removes carrier

  • HPF: removes bias

Rules:

  • \(f_{LPF} > f_{m,\ max}\)

  • \(f_{HPF} > 0\)

Envelope detectors do not work for:

  • Over-modulated signals

  • DSB-SC

Synchronous Detector#

Used for all modulation types.

Multiply by carrier frequency:

  • Shift up: \(f + f_c\)

  • Shift down: \(f - f_c\)

Negative frequencies reflect and double amplitude.

Apply LPF:

  • Choose \(f_{LPF} > f_{m,\ max}\)

Then HPF:

  • Remove DC bias

Final Design#

Components#

  • Multiplier: shifts to baseband

  • LPF: removes high-frequency content

  • HPF: removes bias

Design Rules#

  • Demodulating frequency = carrier frequency

  • \(f_{LPF} \ge f_{m,\ max}\)

  • \(f_{HPF} > 0\) (≈ 10 Hz)

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